Geodesic
Hodge Numbers from Picard–Fuchs Equations
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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Given a variation of Hodge structure over $\mathbb{P}^1$ with Hodge numbers $(1,1,\dots,1)$, we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–Möller–Zorich, by using the local exponents of the corresponding Picard–Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, $\mathrm{K3}$ surfaces and Calabi–Yau threefolds.
Keywords: variation of Hodge structures; Calabi–Yau manifolds. 
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     author = {Charles F. Doran and Andrew Harder and Alan Thompson},
     title = {Hodge {Numbers} from {Picard{\textendash}Fuchs} {Equations}},
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     year = {2017},
     volume = {13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a44/}
}
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Charles F. Doran; Andrew Harder; Alan Thompson. Hodge Numbers from Picard–Fuchs Equations. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a44/

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